Israel Journal of Mathematics

, Volume 101, Issue 1, pp 205–227 | Cite as

Weierstrass factorizations in compact Riemann surfaces

  • Pascual Cutillas Ripoll
  • José María Verde Ramírez


Letν′ be the complementary in a compact Riemann surface ν of a point (or a finite set). In this paper are characterized the subfields, of the field of meromorphic functions inν′, containing sufficient functions to verify a factorization property, similar to that of the classical Weierstrass theorem. It is also seen that the field generated by the Baker functions is not of this type, and the problem is solved of determining the divisors, inν′, of the holomorphic functions admiting Weierstrass factorizations with Baker functions as factors. As an application, a theorem is obtained characterizing the infinite products, of meromorphic functions in ν with bounded degree, which converge normally inν′.


Riemann Surface Compact Subset Holomorphic Function Meromorphic Function Compact Riemann Surface 
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Copyright information

© Hebrew University 1997

Authors and Affiliations

  • Pascual Cutillas Ripoll
    • 1
  • José María Verde Ramírez
    • 1
  1. 1.Department of Pure and Applied MathematicsUniversity of SalamancaSpain

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